{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Pynamical: cobweb plots of the logistic map\n",
    "\n",
    "Author: Geoff Boeing\n",
    "\n",
    "Journal article: Boeing, G. 2016. \"[Visual Analysis of Nonlinear Dynamical Systems: Chaos, Fractals, Self-Similarity and the Limits of Prediction](http://geoffboeing.com/publications/nonlinear-chaos-fractals-prediction/).\" *Systems*, 4 (4), 37. doi:10.3390/systems4040037.\n",
    "\n",
    "Blog post: http://geoffboeing.com/2015/03/chaos-theory-logistic-map/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### To draw these cobweb plots, pynamical does the following:\n",
    "\n",
    "1. Let x = 0.5\n",
    "1. Start on the x-axis at the point (x, 0)\n",
    "1. Draw a vertical line to the red function curve: this point has the coordinates (x, f(x))\n",
    "1. Draw a horizontal line from this point to the gray diagonal line: this point has the coordinates (f(x), f(x))\n",
    "1. Draw a vertical line from this point to the red function curve: this point has the coordinates (f(x), f(f(x)))\n",
    "1. Repeat steps 4 and 5 recursively one hundred times\n",
    "\n",
    "### To draw the red function curve and gray diagonal line, pynamical does the following:\n",
    "\n",
    "Run the logistic map once each for 1000 population values evenly spaced between 0 and 1. This gives us the results of the logistic equation (y values) across the entire range of possible population values (x values). The gray diagonal line is just a plot of y=x."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from pynamical import cobweb_plot\n",
    "import pandas as pd, numpy as np, matplotlib.pyplot as plt, IPython.display as IPdisplay, glob\n",
    "from PIL import Image\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Draw cobweb plots for several values of r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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Pzyc+Pp7s7Gyio6Np1aqV1ZFqRAtfKaUqcfv2beLi4sjNzSU6OpoWLVpYHanGtPCVUqqC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\nuU3hFxYWEh8fz/f+ls+rS0NoP/Vjgkr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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e5ceb97b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cobweb_plot(r=1.0, )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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3HcFPPGE6klM5efIkSUlJ+PooZv41k+sZ/1mNk+HhS/emrxBQlM2VDz4wmFLY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\nKkpow1dKqSihDV8ppaKENnyllIoS/wV1XVVv8ZHvygAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e5cf160358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cobweb_plot(r=2.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lqEeP5N+yJe0TE8lZsoTM2bNvaRlnzpwhOTmZli1bMmPGDPzktNlOQwpfAFB0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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e5cf462940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cobweb_plot(r=3.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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z82Zy9+2jzZ//bDqK8EFtXnmFrJ07yf7ySwAuXLhAYmIisbGxxMXFESrHk4yS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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e5cf493470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cobweb_plot(r=3.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Demonstrate a basin of attraction with three different initial values and same r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+I/ixx0xHcirHjh1j3rx5+PooZvwti2uZ/12Nk+nhS4/mLxFQnMPF994zmFLY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\nhDZ8pZSKEtrwlVIqSmjDV0qpKPFfRhBUGUWjdHYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e5cf56dda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cobweb_plot(r=2.7, cobweb_x=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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3HcFPPGE6klM5efIkSUlJ+PooZv41k+sZ/1mNk+HhS/emrxBQlM2VDz4wmFLY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\nKkpow1dKqSihDV8ppaKENnyllIoS/wV1XVVv8ZHvygAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e5cf5c4e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cobweb_plot(r=2.7, cobweb_x=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ddwQ//rjpSE7l6NGjpKSk4OujmPaPLK5m/nc1TqaHL92avkRAcQ4X3n/fYEph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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e5cf6587f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cobweb_plot(r=2.7, cobweb_x=0.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Now animate it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# configure the animation: 70 rates between 0 and 3.999 plus 15 paused frames each at start and end\n",
    "save_folder = 'images/cobweb-animate'\n",
    "gif_filepath = 'images/animated-logistic-cobweb.gif'\n",
    "start_r = 0\n",
    "end_r = 3.999\n",
    "steps = 70\n",
    "rates = np.linspace(start_r, end_r, steps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# create a plot for each growth rate\n",
    "for n, r in enumerate(rates):\n",
    "    filename = '{:03d}'.format(n)\n",
    "    title = 'Logistic Map Cobweb Plot, r={:.2f}'.format(r)\n",
    "    cobweb_plot(r=r, filename=filename, folder=save_folder, dpi=90, title=title, show=False)\n",
    "    plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# create a tuple of display durations, one for each frame\n",
    "first_last = 100 #show the first and last frames for 100 ms\n",
    "standard_duration = 10 #show all other frames for 10 ms\n",
    "durations = tuple([first_last] + [standard_duration] * (len(rates) - 2) + [first_last])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# load all the static images into a list then save as an animated gif\n",
    "images = [Image.open(image) for image in glob.glob('{}/*.png'.format(save_folder))]\n",
    "gif = images[0]\n",
    "gif.info['duration'] = durations #ms per frame\n",
    "gif.info['loop'] = 0 #how many times to loop (0=infinite)\n",
    "gif.save(fp=gif_filepath, format='gif', save_all=True, append_images=images[1:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# verify that the number of frames in the gif equals the number of image files and durations\n",
    "Image.open(gif_filepath).n_frames == len(images) == len(durations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"images/animated-logistic-cobweb.gif\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "IPdisplay.Image(url=gif_filepath)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
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   "nbconvert_exporter": "python",
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